ME $234$ Fall $2023$ Final Exam

Problem $3(20$ pts; Show your work for partial credits$)$

As shown in figure, air enters the diffuser of a jet engine at $18$kPa,$216K$ with a velocity of $265\frac{m}{s},$ all data corresponding to high$-$altitude flight. The air flows adiabatically through the diffuser, decelerating to a velocity of $50\frac{m}{s}$ at the diffuser exit. Assume steady$-$state operation, the ideal gas model for air, and negligible potential energy effects.

$($a$)$ Determine the temperature of the air at the exit of the diffuser, in K $.$

$($b$)$ If the air undergoes an isentropic process as it flows through the diffuser, determine the pressure of the air at the diffuser exit, in kPa $.$

$($c$)$ If friction were present, would the pressure of the air at the diffuser exit be greater than, less than, or equal to the value found in part $($b$)?$ Explain.